Integrable Systems and Mathematical Physics Seminar, University of
Glasgow, September 22, 2026
John Baez
Second Quantization for the Kepler Problem
The Kepler problem concerns a point particle in an attractive inverse
square force. After a brief review of the classical and quantum
versions of this problem, focused on their hidden symmetries, we turn
to the quantum Kepler problem for a spin-½ particle. We
show that the Hilbert space \(\mathcal{H}\) of bound states for this
problem is unitarily equivalent to the Hilbert space of solutions of a
massless chiral spin-½ particle on the spacetime
\(\mathbb{R} \times S^3\). The fermionic Fock space on
\(\mathcal{H}\) is thus equivalent to the Hilbert space of a massless
chiral spin-½ free quantum field on \(\mathbb{R} \times
S^3\). By modifying the Hamiltonian on this Fock space, we obtain one
that gives the well-known "Madelung rules", which describe the rough
overall structure of the periodic table.
You can see my slides here, check out an
easier talk on this subject,
or read the paper my talk is based on:
© 2026 John Baez
baez@math.removethis.ucr.andthis.edu
